Disentangling Data Contributions to the Precision Measurement of the Largest Leptonic Mixing Angle

Abstract This study examines the precise measurement of the largest leptonic mixing angle $\theta _{23}$ through the analysis of neutrino oscillation data samples. Our findings indicate that the $\overset{{(\_)}}{\nu }_{\mu }\rightarrow \overset{{{ {(}}}\_{{)}}}{\nu }_{e}$ appearance samples, rather than the $\overset{{{ {(}}}\_{{)}}}{\nu }_{\mu }\rightarrow \overset{{{ {(}}}\_{{)}}}{\nu }_{\mu }$ disappearance samples, are sensitive to testing the hypothesis of maximal mixing $\theta _{23} = \pi /4$, particularly if $\theta _{23}$ resides in the higher octant and $\sin ^2\theta _{23} < 0.54$. The former serves as the primary source for determining the octant of the $\theta _{23}$ mixing angle; however, the latter remains relevant for wide-band energy experiments like the Deep Underground Neutrino Experiment (DUNE) if $\theta _{23}$ deviates significantly from the maximal value. In the joint analysis of a coming accelerator-based long-baseline neutrino experiment, namely, Hyper-Kamiokande (T2HK) and DUNE with ultimate precision 1% on $\sin ^{2}\theta _{13}$, utilizing only appearance sub-samples can exclude the maximal mixing and determine the actual octant for about 64% of the currently allowed range of the $\theta _{23}$ angle. We argue, that despite the presence of parameter degeneracy, the precise measurement of $\theta _{23}$ exhibits minimal dependence on other unknown factors, including the CP-violation phase and neutrino mass ordering.